Zhen Li

Zeyu Liu, Yuhang Liu, Guanghao Zhu et al.

Recent advancements in large language models (LLMs) have demonstrated substantial progress in reasoning capabilities, such as DeepSeek-R1, which leverages rule-based reinforcement learning to enhance logical reasoning significantly. However, extending these achievements to multimodal large language models (MLLMs) presents critical challenges, which are frequently more pronounced for Multimodal Small Language Models (MSLMs) given their typically weaker foundational reasoning abilities: (1) the scarcity of high-quality multimodal reasoning datasets, (2) the degradation of reasoning capabilities due to the integration of visual processing, and (3) the risk that direct application of reinforcement learning may produce complex yet incorrect reasoning processes. To address these challenges, we design a novel framework Infi-MMR to systematically unlock the reasoning potential of MSLMs through a curriculum of three carefully structured phases and propose our multimodal reasoning model Infi-MMR-3B. The first phase, Foundational Reasoning Activation, leverages high-quality textual reasoning datasets to activate and strengthen the model's logical reasoning capabilities. The second phase, Cross-Modal Reasoning Adaptation, utilizes caption-augmented multimodal data to facilitate the progressive transfer of reasoning skills to multimodal contexts. The third phase, Multimodal Reasoning Enhancement, employs curated, caption-free multimodal data to mitigate linguistic biases and promote robust cross-modal reasoning. Infi-MMR-3B achieves both state-of-the-art multimodal math reasoning ability (43.68% on MathVerse testmini, 27.04% on MathVision test, and 21.33% on OlympiadBench) and general reasoning ability (67.2% on MathVista testmini). Resources are available at https://huggingface.co/Reallm-Labs/Infi-MMR-3B.

Jiefeng Zhou, Zhen Li, Yong Deng

Random walk is an explainable approach for modeling natural processes at the molecular level. The Random Permutation Set Theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer Theory. Recent explorations indicate a promising link between RPST and random walk. In this study, we conduct an analysis and construct a random walk model based on the properties of RPST, with Monte Carlo simulations of such random walk. Our findings reveal that the random walk generated through RPST exhibits characteristics similar to those of a Gaussian random walk and can be transformed into a Wiener process through a specific limiting scaling procedure. This investigation establishes a novel connection between RPST and random walk theory, thereby not only expanding the applicability of RPST, but also demonstrating the potential for combining the strengths of both approaches to improve problem-solving abilities.

Jiefeng Zhou, Zhen Li, Kang Hao Cheong et al.

The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been proposed. Exploring the maximum entropy provides a possible way of understanding the physical meaning of RPS. In this paper, a new concept, the envelope of entropy function, is defined. In addition, the limit of the envelope of RPS entropy is derived and proved. Compared with the existing method, the computational complexity of the proposed method to calculate the envelope of RPS entropy decreases greatly. The result shows that when $N \to \infty$, the limit form of the envelope of the entropy of RPS converges to $e \times (N!)^2$, which is highly connected to the constant $e$ and factorial. Finally, numerical examples validate the efficiency and conciseness of the proposed envelope, which provides a new insight into the maximum entropy function.